Overview

abstract

In this work, we address the following question:¿ When can we guarantee the optimality of
linear coding at all internal nodes of a network?¿ While sufficient conditions for linear coding
throughout the network are known, it is not clear whether relaxing the linearity constraints at
the terminal nodes can result in simpler operations at the internal nodes. We present a novel
method to analyze the space of network solutions using the constraints resulting from the
network topology, and we identify sufficient conditions for an optimal linear solution at all
internal nodes. These conditions are also sufficient to characterize the rate region only in
terms of Shannon information inequalities.